scholarly journals Graphs with Four Boundary Vertices

10.37236/498 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Tobias Müller ◽  
Attila Pór ◽  
Jean-Sébastien Sereni
Keyword(s):  
Positive Integer ◽  
Full Description ◽  
Boundary Vertex ◽  
Induced Subgraph ◽  
Distance Vector

A vertex $v$ of a graph $G$ is a boundary vertex if there exists a vertex $u$ such that the distance in $G$ from $u$ to $v$ is at least the distance from $u$ to any neighbour of $v$. We give a full description of all graphs that have exactly four boundary vertices, which answers a question of Hasegawa and Saito. To this end, we introduce the concept of frame of a graph. It allows us to construct, for every positive integer $b$ and every possible "distance-vector" between $b$ points, a graph $G$ with exactly $b$ boundary vertices such that every graph with $b$ boundary vertices and the same distance-vector between them is an induced subgraph of $G$.

scholarly journals Major n-connected graphs

1989 ◽  
Vol 47 (1) ◽  
pp. 43-52
Author(s):  
Ortrud R. Oellermann
Keyword(s):  
Positive Integer ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Connected Subgraph ◽  
Edge Connectivity ◽  
Maximum Order ◽  
Induced Subgraph ◽  
Connected Graphs

AbstractAn induced subgraph H of connectivity (edge-connectivity) n in a graph G is a major n-connected (major n-edge-connected) subgraph of G if H contains no subgraph with connectivity (edge- connectivity) exceeding n and H has maximum order with respect to this property. An induced subgraph is a major (major edge-) subgraph if it is a major n-connected (major n-edge-connected) subgraph for some n. Let m be the maximum order among all major subgraphs of C. Then the major connectivity set K(G) of G is defined as the set of all n for which there exists a major n-connected subgraph of G having order m. The major edge-connectivity set is defined analogously. The connectivity and the elements of the major connectivity set of a graph are compared, as are the elements of the major connectivity set and the major edge-connectivity set of a graph. It is shown that every set S of nonnegative integers is the major connectivity set of some graph G. Further, it is shown that for each positive integer m exceeding every element of S, there exists a graph G such that every major k-connected subgraph of G, where k ∈ K(G), has order m. Moreover, upper and lower bounds on the order of such graphs G are established.

scholarly journals Thin Lehman Matrices and Their Graphs

10.37236/437 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Jonathan Wang
Keyword(s):  
Positive Integer ◽  
Maximum Clique ◽  
Circulant Matrix ◽  
Complete Classification ◽  
Connected Components ◽  
Connected Component ◽  
Johnson Graph ◽  
Induced Subgraph ◽  
The Matrix

Two square $0,1$ matrices $A,B$ are a pair of Lehman matrices if $AB^T = J+dI$, where $J$ is the matrix of all $1$s and $d$ is a positive integer. It is known that there are infinitely many such matrices when $d=1$, and these matrices are called thin Lehman matrices. An induced subgraph of the Johnson graph may be defined given any Lehman matrix, where the vertices of the graph correspond to rows of the matrix. These graphs are used to study thin Lehman matrices. We show that any connected component of such a graph determines the corresponding rows of the matrix up to permutations of the columns. We also provide a sharp bound on the maximum clique size of such graphs and give a complete classification of Lehman matrices whose graphs have at most two connected components. Some constraints on when a circulant matrix can be Lehman are also provided. Many general classes of thin Lehman matrices are constructed in the paper.

scholarly journals On $(\delta, \chi)$-Bounded Families of Graphs

10.37236/595 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
András Gyárfás ◽  
Manouchehr Zaker
Keyword(s):  
Positive Integer ◽  
Chromatic Number ◽  
Minimum Degree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Induced Subgraph ◽  
The Family ◽  
Infinite Collection ◽  
Delta G ◽  
Necessary And Sufficient

A family ${\mathcal{F}}$ of graphs is said to be $(\delta,\chi)$-bounded if there exists a function $f(x)$ satisfying $f(x)\rightarrow \infty$ as $x\rightarrow \infty$, such that for any graph $G$ from the family, one has $f(\delta(G))\leq \chi(G)$, where $\delta(G)$ and $\chi(G)$ denotes the minimum degree and chromatic number of $G$, respectively. Also for any set $\{H_1, H_2, \ldots, H_k\}$ of graphs by $Forb(H_1, H_2, \ldots, H_k)$ we mean the class of graphs that contain no $H_i$ as an induced subgraph for any $i=1, \ldots, k$. In this paper we first answer affirmatively the question raised by the second author by showing that for any tree $T$ and positive integer $\ell$, $Forb(T, K_{\ell, \ell})$ is a $(\delta, \chi)$-bounded family. Then we obtain a necessary and sufficient condition for $Forb(H_1, H_2, \ldots, H_k)$ to be a $(\delta, \chi)$-bounded family, where $\{H_1, H_2, \ldots, H_k\}$ is any given set of graphs. Next we study $(\delta, \chi)$-boundedness of $Forb({\mathcal{C}})$ where ${\mathcal{C}}$ is an infinite collection of graphs. We show that for any positive integer $\ell$, $Forb(K_{\ell,\ell}, C_6, C_8, \ldots)$ is $(\delta, \chi)$-bounded. Finally we show a similar result when ${\mathcal{C}}$ is a collection consisting of unicyclic graphs.

X-ray mapping without STEM

1994 ◽  
Vol 52 ◽  
pp. 508-509
Author(s):  
Judith M. Brock ◽  
Max T. Otten
Keyword(s):  
Life Science ◽  
Materials Science ◽  
Chemical Elements ◽  
Full Description ◽  
Scanning System ◽  
Elemental Distribution ◽  
X Ray ◽  
Transmission Electron ◽  
Distribution Of Elements ◽  
Made In

A knowledge of the distribution of chemical elements in a specimen is often highly useful. In materials science specimens features such as grain boundaries and precipitates generally force a certain order on mental distribution, so that a single profile away from the boundary or precipitate gives a full description of all relevant data. No such simplicity can be assumed in life science specimens, where elements can occur various combinations and in different concentrations in tissue. In the latter case a two-dimensional elemental-distribution image is required to describe the material adequately. X-ray mapping provides such of the distribution of elements.The big disadvantage of x-ray mapping hitherto has been one requirement: the transmission electron microscope must have the scanning function. In cases where the STEM functionality – to record scanning images using a variety of STEM detectors – is not used, but only x-ray mapping is intended, a significant investment must still be made in the scanning system: electronics that drive the beam, detectors for generating the scanning images, and monitors for displaying and recording the images.

ARIMA(p,d,q) and Non-Linear Approximation Models for the Fractal Dimension of the Density of Primes Less or Equal to a Positive Integer

2013 ◽  
Vol 1 (2) ◽  
pp. 177-191
Author(s):  
Roberto Padua ◽  
Rodel Azura ◽  
Mark Borres ◽  
Adriano Patac Jr. ◽  
◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Positive Integer ◽  
Linear Approximation ◽  
Non Linear ◽  
Approximation Models

A Survey Study on Attacks in MANET Ad-Hoc Network

2017 ◽  
Vol 7 (7) ◽  
pp. 387
Author(s):  
. Harpal ◽  
Gaurav Tejpal ◽  
Sonal Sharma
Keyword(s):  
Routing Protocol ◽  
Ad Hoc Network ◽  
Ad Hoc ◽  
Mobile Ad Hoc Network ◽  
Survey Study ◽  
Short Article ◽  
The People ◽  
Distance Vector ◽  
Mobile Ad Hoc ◽  
Real World Problems

In this time of instant units, Mobile Ad-hoc Network(MANET) has become an indivisible part for transmission for mobile devices. Therefore, curiosity about study of Mobile Ad-hoc Network has been growing because last several years. In this report we have mentioned some simple routing protocols in MANET like Destination Sequenced Distance Vector, Active Source Redirecting, Temporally-Ordered Redirecting Algorithm and Ad-hoc On Need Distance Vector. Protection is just a serious problem in MANETs because they are infrastructure-less and autonomous. Principal target of writing this report is to handle some simple problems and security considerations in MANET, operation of wormhole strike and acquiring the well-known routing protocol Ad-hoc On Need Distance Vector. This short article will be a great help for the people performing study on real world problems in MANET security.

General Cluster Sorption Isotherm

2020 ◽  
Author(s):  
Christoph Buttersack
Keyword(s):  
Density Functional ◽  
Capillary Condensation ◽  
Cluster Formation ◽  
Full Range ◽  
Full Description ◽  
Cross Sectional ◽  
Macroporous Silica ◽  
Isotherm Equation ◽  
Type Iv ◽  
Classical Thermodynamics

<p>Adsorption isotherms are an essential tool in chemical physics of surfaces. However, several approaches based on a different theoretical basis exist and for isotherms including capillary condensation existing approaches can fail. Here, a general isotherm equation is derived and applied to literature data both concerning type IV isotherms of argon and nitrogen in ordered mesoporous silica, and type II isotherms of disordered macroporous silica. The new isotherm covers the full range of partial pressure (10<sup>-6</sup> - 0.7). It relies firstly on the classical thermodynamics of cluster formation, secondly on a relationship defining the free energy during the increase of the cluster size. That equation replaces the Lennard-Jones potentials used in the classical density functional theory. The determination of surface areas is not possible by this isotherm because the cross-sectional area of a cluster is unknown. Based on the full description of type IV isotherms, most known isotherms are accessible by respective simplifications. </p>

The Order of Monochromatic Subgraphs with a Given Minimum Degree

10.37236/1725 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Yair Caro ◽  
Raphael Yuster
Keyword(s):  
Positive Integer ◽  
Minimum Degree

Let $G$ be a graph. For a given positive integer $d$, let $f_G(d)$ denote the largest integer $t$ such that in every coloring of the edges of $G$ with two colors there is a monochromatic subgraph with minimum degree at least $d$ and order at least $t$. Let $f_G(d)=0$ in case there is a $2$-coloring of the edges of $G$ with no such monochromatic subgraph. Let $f(n,k,d)$ denote the minimum of $f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and minimum degree at least $k$. In this paper we establish $f(n,k,d)$ whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large. We also consider the case where more than two colors are allowed.

Extensions of Rings Having McCoy Condition

2009 ◽  
Vol 52 (2) ◽  
pp. 267-272 ◽  
Author(s):  
Muhammet Tamer Koşan
Keyword(s):  
Positive Integer ◽  
Associative Ring ◽  
Nonzero Element ◽  
Ring Extensions

AbstractLet R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f (x)g(x) = 0 (over R[x]), where 0 ≠ f (x), g(x) ∈ R[x], implies that there exists a nonzero element c ∈ R such that f (x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy ring, then R[x]/(xn) is a right McCoy ring for any positive integer n ≥ 2.

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